大多边形空间
Big polygon spaces
AI总结：
本文提出新的紧致可定向流形“大多边形空间”，研究其等变上同调的特殊性质，证明了相关合冲阶界的紧性。
摘要：
我们研究一类新的紧致可定向流形，称为大多边形空间。它们是实二次曲面的交，与多边形空间相关，后者是大多边形空间在典范环面作用下的不动点集。\n 大多边形空间的有趣之处在于它们在等变上同调中展现出显著的新特性：尽管其等变上同调作为BT上同调环上的模绝非自由模，但Chang-Skjelbred序列对它们可以是正合的，且等变庞加莱配对是完美的。更一般地，大多边形空间表明，由Allday、Puppe与本文作者得到的、关于紧致可定向T-流形等变上同调的合冲阶的某一界是紧的。
英文摘要：
We study a new class of compact orientable manifolds, called big polygon spaces. They are intersections of real quadrics and related to polygon spaces, which appear as their fixed point set under a canonical torus action. What makes big polygon spaces interesting is that they exhibit remarkable new features in equivariant cohomology: The Chang-Skjelbred sequence can be exact for them and the equivariant Poincare pairing perfect although their equivariant cohomology is never free as a module over the cohomology ring of BT. More generally, big polygon spaces show that a certain bound on the syzygy order of the equivariant cohomology of compact orientable T-manifolds obtained by Allday, Puppe and the author is sharp.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
